Time signature

An example of a 34 time signature. The time signature indicates that there are three quarter notes (crotchets) per measure (bar).

The time signature (also known as meter signature,[1]metre signature,[2] or measure signature)[3] is a notational convention used in Westernmusical notation to specify how many beats (pulses) are contained in each measure (bar), and which note value is equivalent to a beat.

In a music score, the time signature appears at the beginning as a time symbol or stacked numerals, such as or 34 (read common time and three-four time, respectively), immediately following the key signature (or immediately following the clef symbol if the key signature is empty). A mid-score time signature, usually immediately following a barline, indicates a change of meter.

For instance, 24 means two quarter-note (crotchet) beats per bar, while 38 means three eighth-note (quaver) beats per bar. The most common simple time signatures are 24, 34, and 44.

By convention, two special symbols are sometimes used for 44 and 22:

The symbol is sometimes used for 44 time, also called common time or imperfect time. The symbol is derived from a broken circle used in music notation from the 14th through 16th centuries, where a full circle represented what today would be written in 32 or 34 time, and was called tempus perfectum (perfect time).[4] See Mensural time signatures below.

The symbol is also a carry-over from the notational practice of late-Medieval and Renaissance music, where it signified tempus imperfectum diminutum (diminished imperfect time)—more precisely, a doubling of the speed, or proportio dupla, in duple meter.[5] In modern notation, it is used in place of 22 and is called alla breve or, colloquially, cut time or cut common time.

In compound meter, subdivisions (which are what the upper number represents in these meters) of the beat are in three equal parts, so that a dotted note (half again longer than a regular note) becomes the beat. The upper numeral of compound time signatures is commonly 3, 6, 9, or 12 (multiples of 3 in each beat). The lower number is most commonly an 8 (an eighth-note or quaver): as in 98 or 128.

Time signatures indicating two beats per bar (whether in simple or compound meter) are called duple meter, while those with three beats to the bar are triple meter. Terms such as quadruple (4), quintuple (5), and so on, are also occasionally used.

To the ear, a bar may seem like one singular beat. For example, a fast waltz, notated in 34 time, may be described as being one in a bar. Correspondingly, at slow tempos, the beat indicated by the time signature could in actual performance be divided into smaller units.

On a formal mathematical level, the time signatures of, e.g., 34 and 38 are interchangeable. In a sense, all simple triple time signatures, such as 38, 34, 32, etc.—and all compound duple times, such as 68, 616 and so on, are equivalent. A piece in 34 can be easily rewritten in 38, simply by halving the length of the notes.

Other time signature rewritings are possible: most commonly a simple time signature with triplets translates into a compound meter.

Though formally interchangeable, for a composer or performing musician, by convention, different time signatures often have different connotations. First, a smaller note value in the beat unit implies a more complex notation, which can affect ease of performance. Second, beaming affects the choice of actual beat divisions. It is, for example, more natural to use the quarter note/crotchet as a beat unit in 64 or 22 than the eight/quaver in 68 or 24.[citation needed] Third, time signatures are traditionally associated with different music styles—it might seem strange to notate a rock tune in 48 or 42.

Signatures that do not fit the usual duple or triple categories are called complex, asymmetric, irregular, unusual, or odd—though these are broad terms, and usually a more specific description is appropriate.[citation needed] The term odd meter, however, sometimes describes time signatures in which the upper number is simply odd rather than even, including 34 and 98.[8]

The irregular meters (not fitting duple or triple categories) are common in some non-Western music, but rarely appeared in formal written Western music until the 19th century. Early anomalous examples appeared in Spain between 1516 and 1520,[8] but the Delphic Hymns to Apollo (one by Athenaeus is entirely in quintuple meter, the other by Limenius predominantly so), carved on the exterior walls of the Athenian Treasury at Delphi in 128 BC are in the relatively common cretic meter, with five beats to a foot.[9]

However, such time signatures are only unusual in most Western music. Traditional music of the Balkans uses such meters extensively. Bulgarian dances, for example, include forms with 5, 7, 9, 11, 13, 15, 22, 25 and other numbers of beats per measure. These rhythms are notated as additive rhythms based on simple units, usually 2, 3 and 4 beats, though the notation fails to describe the metric "time bending" taking place, or compound meters. See Additive meters below.

While time signatures usually express a regular pattern of beat stresses continuing through a piece (or at least a section), sometimes composers place a different time signature at the beginning of each bar, resulting in music with an extremely irregular rhythmic feel. In this case, the time signatures are an aid to the performers and not necessarily an indication of meter. The Promenade from Modest Mussorgsky's Pictures at an Exhibition (1874) is a good example. The opening measures are shown below:

Some pieces have no time signature, as there is no discernible meter. This is sometimes known as free time. Sometimes one is provided (usually 44) so that the performer finds the piece easier to read, and simply has "free time" written as a direction. Sometimes the word FREE is written downwards on the staff to indicate the piece is in free time. Erik Satie wrote many compositions that are ostensibly in free time but actually follow an unstated and unchanging simple time signature. Later composers used this device more effectively, writing music almost devoid of a discernibly regular pulse.

If two time signatures alternate repeatedly, sometimes the two signatures are placed together at the beginning of the piece or section, as shown below:

To indicate more complex patterns of stresses, such as additive rhythms, more complex time signatures can be used. Additive meters have a pattern of beats that subdivide into smaller, irregular groups. Such meters are sometimes called imperfect, in contrast to perfect meters, in which the bar is first divided into equal units.[14]

For example, the time signature 3+2+38 means that there are 8 quaver beats in the bar, divided as the first of a group of three eighth notes (quavers) that are stressed, then the first of a group of two, then first of a group of three again. The stress pattern is usually counted as

3+2+38: one two three one two one two three ...

This kind of time signature is commonly used to notate folk and non-Western types of music. In classical music, Béla Bartók and Olivier Messiaen have used such time signatures in their works. The first movement of Maurice Ravel's Piano Trio in A Minor is written in 88, in which the beats are likewise subdivided into 3+2+3 to reflect Basque dance rhythms.

Romanian musicologistConstantin Brăiloiu had a special interest in compound time signatures, developed while studying the traditional music of certain regions in his country. While investigating the origins of such unusual meters, he learned that they were even more characteristic of the traditional music of neighboring peoples (e.g., the Bulgarians). He suggested that such timings can be regarded as compounds of simple two-beat and three-beat meters, where an accent falls on every first beat, even though, for example in Bulgarian music, beat lengths of 1, 2, 3, 4 are used in the metric description. In addition, when focused only on stressed beats, simple time signatures can count as beats in a slower, compound time. However, there are two different-length beats in this resulting compound time, a one half-again longer than the short beat (or conversely, the short beat is ​2⁄3 the value of the long). This type of meter is called aksak (the Turkish word for "limping"), impeded, jolting, or shaking, and is described as an irregular bichronic rhythm. A certain amount of confusion for Western musicians is inevitable, since a measure they would likely regard as 716, for example, is a three-beat measure in aksak, with one long and two short beats (with subdivisions of 2+2+3, 2+3+2, or 3+2+2).[15]

Folk music may make use of metric time bends, so that the proportions of the performed metric beat time lengths differ from the exact proportions indicated by the metric. Depending on playing style of the same meter, the time bend can vary from non-existent to considerable; in the latter case, some musicologists may want to assign a different meter. For example, the Bulgarian tune "Eleno Mome" is written in one of three forms: (1) 7 = 2+2+1+2, (2) 13 = 4+4+2+3, or (3) 12 = 3+4+2+3, but an actual performance (e.g., Smithsonian Eleno Mome) may be closer to 4+4+2+3. The Macedonian 3+2+2+3+2 meter is even more complicated, with heavier time bends, and use of quadruples on the threes. The metric beat time proportions may vary with the speed that the tune is played. The Swedish Boda Polska (Polska from the parish Boda) has a typical elongated second beat.

In Western classical music, metric time bend is used in the performance of the Viennese Waltz. Most Western music uses metric ratios of 2:1, 3:1, or 4:1 (two-, three- or four-beat time signatures)—in other words, integer ratios that make all beats equal in time length. So, relative to that, 3:2 and 4:3 ratios correspond to very distinctive metric rhythm profiles. Complex accentuation occurs in Western music, but as syncopation rather than as part of the metric accentuation.[citation needed]

Brăiloiu borrowed a term from Turkish medieval music theory: aksak. Such compound time signatures fall under the "aksak rhythm" category that he introduced along with a couple more that should describe the rhythm figures in traditional music.[16] The term Brăiloiu revived had moderate success worldwide, but in Eastern Europe it is still frequently used. However, aksak rhythm figures occur not only in a few European countries, but on all continents, featuring various combinations of the two and three sequences. The longest are in Bulgaria. The shortest aksak rhythm figures follow the five-beat timing, comprising a two and a three (or three and two).

The rhythm of Dave Brubeck's "Blue Rondo à la Turk": It consists of three measures of 2+2+2+3 followed by one measure of 3+3+3 and the cycle then repeats. Taking the smallest time unit as eighth notes, the arrows on the tempo dial show the tempi for ♪, ♩, ♩. and the measure beat. Starts slow, speeds up to usual tempo

A method to create meters of lengths of any length has been published in the Journal of Anaphoria Music Theory [17]And Xenharmonikon 16[18] using both those based on the Horograms of Erv Wilson and Viggo Brun's algorithm written by Kraig Grady.

Example of an irrational 43 time signature: here there are four (4) third notes (3) per measure. A "third note" would be one third of a whole note, and thus is a half-note triplet. The second measure of 42 presents the same notes, so the 43 time signature serves to indicate the precise speed relationship between the notes in the two measures.

Irrational time signatures (rarely, "non-dyadic time signatures") are used for so-called irrational bar lengths,[19] that have a denominator that is not a power of two (1, 2, 4, 8, 16, 32, etc.). These are based on beats expressed in terms of fractions of full beats in the prevailing tempo—for example 310 or 524.[19] For example, where 44 implies a bar construction of four quarter-parts of a whole note (i.e., four quarter notes), 43 implies a bar construction of four third-parts of it. These signatures are of utility only when juxtaposed with other signatures with varying denominators; a piece written entirely in 43, say, could be more legibly written out in 44.

The same example written using metric modulation instead of irrational time signatures. Three half notes in the first measure (making up a dotted whole note) are equal in duration to two half notes in the second (making up a whole note).

The same example written using a change in time signature.

According to Brian Ferneyhough, metric modulation is "a somewhat distant analogy" to his own use of "irrational time signatures" as a sort of rhythmic dissonance.[19] It is arguable whether the use of these signatures makes metric relationships clearer or more obscure to the musician; it is always possible to write a passage using non-irrational signatures by specifying a relationship between some note length in the previous bar and some other in the succeeding one. Sometimes, successive metric relationships between bars are so convoluted that the pure use of irrational signatures would quickly render the notation extremely hard to penetrate. Good examples, written entirely in conventional signatures with the aid of between-bar specified metric relationships, occur a number of times in John Adams' opera Nixon in China (1987), where the sole use of irrational signatures would quickly produce massive numerators and denominators.[citation needed]

Historically, this device has been prefigured wherever composers wrote tuplets. For example, a 24 bar of 3 triplet crotchets could arguably be written as a bar of 36. Henry Cowell's piano piece Fabric (1920) employs separate divisions of the bar (anything from 1 to 9) for the three contrapuntal parts, using a scheme of shaped noteheads to visually clarify the differences, but the pioneering of these signatures is largely due to Brian Ferneyhough, who says that he finds that "such 'irrational' measures serve as a useful buffer between local changes of event density and actual changes of base tempo".[19]Thomas Adès has also used them extensively—for example in Traced Overhead (1996), the second movement of which contains, among more conventional meters, bars in such signatures as 26, 914 and 524.

Notationally, rather than using Cowell's elaborate series of notehead shapes, the same convention has been invoked as when normal tuplets are written; for example, one beat in 45 is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only ​4⁄5 of a reference whole note, and a beat ​1⁄5 of one (or ​4⁄5 of a normal quarter note). This is notated in exactly the same way that one would write if one were writing the first four quarter notes of five quintuplet quarter notes.

Some video samples are shown below.

These video samples show two time signatures combined to make a polymeter, since 43, say, in isolation, is identical to 44.

Music educator Carl Orff proposed replacing the lower number of the time signature with an actual note image, as shown at right. This system eliminates the need for compound time signatures, which are confusing to beginners. While this notation has not been adopted by music publishers generally (except in Orff's own compositions), it is used extensively in music education textbooks. Similarly, American composers George Crumb and Joseph Schwantner, among others, have used this system in many of their works.

Another possibility is to extend the barline where a time change is to take place above the top instrument's line in a score and to write the time signature there, and there only, saving the ink and effort that would have been spent writing it in each instrument's staff. Henryk Górecki's Beatus Vir is an example of this. Alternatively, music in a large score sometimes has time signatures written as very long, thin numbers covering the whole height of the score rather than replicating it on each staff; this is an aid to the conductor, who can see signature changes more easily.

In the 14th, 15th and 16th centuries, a period in which mensural notation was used, four basic mensuration signs determined the proportion between the two main units of rhythm. There were no measure or bar lines in music of this period; these signs, the ancestors of modern time signatures, indicate the ratio of duration between different note values. The relation between the breve and the semibreve was called tempus, and the relation between the semibreve and the minim was called prolatio. The breve and the semibreve use roughly the same symbols as our modern double whole note (breve) and whole note (semibreve), but they were not limited to the same proportional values as are in use today. There are complicated rules concerning how a breve is sometimes three and sometimes two semibreves. Unlike modern notation, the duration ratios between these different values was not always 2:1; it could be either 2:1 or 3:1, and that is what, amongst other things, these mensuration signs indicated. A ratio of 3:1 was called complete, perhaps a reference to the Trinity, and a ratio of 2:1 was called incomplete.

A circle used as a mensuration sign indicated tempus perfectum (a circle being a symbol of completeness), while an incomplete circle, resembling a letter C, indicated tempus imperfectum. Assuming the breve is a beat, this corresponds to the modern concepts of triple meter and duple meter, respectively. In either case, a dot in the center indicated prolatio perfecta (compound meter) while the absence of such a dot indicated prolatio imperfecta (simple meter).

A rough equivalence of these signs to modern meters would be:

corresponds to 98 meter;

corresponds to 34 meter;

corresponds to 68 meter;

corresponds to 24 meter.

N.B.: in modern compound meters the beat is a dotted note value, such as a dotted quarter, because the ratios of the modern note value hierarchy are always 2:1. Dotted notes were never used in this way in the mensural period; the main beat unit was always a simple (undotted) note value.

or just proportio tripla, 1:3 proportion (three times as fast, similar to triplets).

Often the ratio was expressed as two numbers, one above the other,[22] looking similar to a modern time signature, though it could have values such as 43, which a conventional time signature could not.

Some proportional signs were not used consistently from one place or century to another. In addition, certain composers delighted in creating "puzzle" compositions that were intentionally difficult to decipher.[23]

In particular, when the sign was encountered, the tactus (beat) changed from the usual whole note (semibreve) to the double whole note (breve), a circumstance called alla breve. This term has been sustained to the present day, and though now it means the beat is a half note (minim), in contradiction to the literal meaning of the phrase, it still indicates that the beat has changed to a longer note value.